Simplify the following expression: $ q = \dfrac{7}{4} + \dfrac{-10p + 3}{-6p} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6p}{-6p}$ $ \dfrac{7}{4} \times \dfrac{-6p}{-6p} = \dfrac{-42p}{-24p} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-10p + 3}{-6p} \times \dfrac{4}{4} = \dfrac{-40p + 12}{-24p} $ Therefore $ q = \dfrac{-42p}{-24p} + \dfrac{-40p + 12}{-24p} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-42p - 40p + 12}{-24p} $ $q = \dfrac{-82p + 12}{-24p}$ Simplify the expression by dividing the numerator and denominator by -2: $q = \dfrac{41p - 6}{12p}$